'Umar came near the Black Stone and kissed it and said “No doubt, I know that you are a stone and can neither benefit anyone nor harm anyone. Had I not seen Allah’s Apostle kissing you I would not have kissed you.”
There is no benefit in kissing the black stone, so it does not remove sins either. Hazrat Umar RA himself did not know why the prophet kissed the stone but he did it because it was something the prophet did and he wanted to emulate the prophet. Also it is not obligatory to kiss the stone or touch it during Hajj or Umrah.
You explained the cross well and that makes sense but again there is a difference between the actual item and a picture of that item.